Correct Answer - D
The tangent at (1, 7) to the parabola `x^(2) = y - 6x` is
`x (1) = (1)/(2) (y + 7) - 6`
[replacing `x^(2) to xx_(1)` and `2y to y + y_(1)`]
`implies 2x = y + 7 - 12`
`implies y = 2x + 5`
Which is also tangents to the circle
`x^(2) + y^(2) + 16x + 12 y + c = 0`
i.e., `x^(2) + (2x + 5)^(2) + 16x + 12 (2x + 5) + C = 0` must have equal, rools i.e., `alpha = beta`
`implies 5x^(2) + 60x + 85 + c = 0`
`implies alpha + beta = (-60)/(5)`
`implies alpha = - 6`
`:. x = - 6` and `y = 2x + 5 = - 7`
`:.` Point of contact is (-6, -7).
